In this paper, we present a high quality and interactive method for volume rendering curvilinear-grid datasets. This method is based on a two-stage parallel transformation of the sample position into intermediate computational space then into texture space through the use of multiple 1 and 2D deformation textures using hardware acceleration. In this manner, it is possible to render many curvilinear-grid volume datasets at high quality and with a low memory footprint, while taking advantage of modern graphic hardware's tri-linear filtering for the data itself. We also extend our method to handle volume shading. We present a comprehensive study and comparisons with previous works, we show improvements both in quality and performance using our technique on multiple curvilinear datasets.